The Calabi invariant for Hamiltonian diffeomorphisms of the unit disk

2021/02/18 by B. Joly, Joly, Benoît
Mathematics · #Geometric and Algebraic Topology #Geometry and complex manifolds #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2102.09352

Abstract

In this article, we study the Calabi invariant on the unit disk usually defined on compactly supported Hamiltonian diffeomorphisms of the open disk. In particular we extend the Calabi invariant to the group of C¹ diffeomorphisms of the closed disk which preserves the standard symplectic form. We also compute the Calabi invariant for some diffeomorphisms of the disk which satisfies some rigidity hypothesis.

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